Rule: Q[7, 56]

Type

Polynomials

One starts from the polynomial $P_1$ and extends one by one with $P_{\mathrm{i}}$ until the final polynomial defining this rule is reached.
Note: Polynomials might be truncated due to size! The complete polynomials are included in the download.

• $P_1$:
  $128\cdot t^7-192\cdot t^5+80\cdot t^3-8\cdot t$
• $P_2$:
  $128\cdot t^{63}-1984\cdot t^{61}+14640\cdot t^{59}-68440\cdot t^{57}+227563\cdot t^{55}-\frac{1145529}{2}\cdot t^{53}+\frac{9072063}{8}\cdot t^{51}-\frac{28989675}{16}\cdot t^{49}+\frac{608783175}{256}\cdot t^{47}-\frac{1329484065}{512}\cdot t^{45}+\frac{4874774905}{2048}\cdot t^{43}-\frac{7550466105}{4096}\cdot t^{41}+\frac{39688347475}{32768}\cdot t^{39}-\frac{44357564825}{65536}\cdot t^{37}+\frac{84406109067}{262144}\cdot t^{35}-\frac{68328754959}{524288}\cdot t^{33}+\frac{751616304549}{16777216}\cdot t^{31}-\frac{437423756715}{33554432}\cdot t^{29}+\frac{428971123735}{134217728}\cdot t^{27}-\frac{176103935007}{268435456}\cdot t^{25}+\frac{240141729555}{2147483648}\cdot t^{23}-\frac{67282234305}{4294967296}\cdot t^{21}+\frac{30582833775}{17179869184}\cdot t^{19}-\frac{5545773675}{34359738368}\cdot t^{17}+\frac{6285210165}{549755813888}\cdot t^{15}-\frac{676868787}{1099511627776}\cdot t^{13}+\frac{106874019}{4398046511104}\cdot t^{11}-\frac{5883955}{8796093022208}\cdot t^9+\frac{840565}{70368744177664}\cdot t^7-\frac{17391}{140737488355328}\cdot t^5+\frac{341}{562949953421312}\cdot t^3-\frac{1}{1125899906842624}\cdot t$

Node locations in the complex plane

Magnitude of the Weights

Quadrature Rule Data

Nodes

Weights

Download

All rules of Chebyshev U (second kind) type can be downloaded here packed into a single file.